Ambjorn / Carfora / Marzuoli The Geometry of Dynamical Triangulations

Erscheinungsjahr 2009
ISBN: 978-3-540-69427-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 50, 197 Seiten, eBook

Reihe: Lecture Notes in Physics Monographs

The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.

Zielgruppe

Research

Autoren/Hrsg.

Ambjorn, Jan

Carfora, Mauro

Marzuoli, Annalisa

Inhaltsverzeichnis

Triangulations.- Dynamical Triangulations.- Moduli Spaces for Dynamically Triangulated Manifolds.- Curvature Assignments for Dynamical Triangulations.- Entropy Estimates.- Analytical vs. Numerical Data.